The S&P 500 Index set several new all-time highs in 2015, with the most recent one coming on May 21, 2015. Each new record high, especially for an extended bull market, begs investors to ask if the stock market is at its peak and poised to move lower. No one wants to buy at a top, watch price declines unfold, and wait an extended period just to recoup losses. How likely is that scenario? What exactly is the risk of buying at the top when there is an all-time high? We attempt to answer these questions. “Buy low, sell high” is one of the most recognizable stock market sayings. Investing when markets are at all-time highs would seem to fly directly in the face of this saying, leading many investors to believe that investing at all-time highs is a sure way to lose money. But is this really the case? Buying at an all-time high, especially several years into a bull market, can be unnerving. But looking at the odds that anygiven all-time high is followed by another all-time high within a certain time period can be reassuring. Analysis of the S&P 500 Index indicates that from the date of any given all-time high, the index has historically hit another all-time high within one month 91% of the time. Extending this time frame to three months increases those odds to over 97%, and extending to one year the odds approach 99%. Based on those odds, you have a very good chance of seeing another all-time high pretty soon after you buy on one….